Four spheres of diameter 2a and mass M each are placed with their centres at four corners of a square of side b. Calculate the moment of inertia of the system about one side of the square taken as its axis ?

Here I

_{cm}for any sphere is ${I}_{cm}=\frac{2}{5}M{a}^{2}$

If one side of square is taken as axis then moment of inertia about this axis is given by

$I={I}_{cm}+M{b}^{2}\phantom{\rule{0ex}{0ex}}I=\frac{2}{5}M{a}^{2}+M{b}^{2}..........\left(1\right)forasphereaboutaxisofrotation$

Hence required moment of inertia is

${I}_{net}=2\left(\frac{2}{5}M{a}^{2}\right)+2(\frac{2}{5}M{a}^{2}+M{b}^{2})=\frac{8}{5}M{a}^{2}+2M{b}^{2}=\frac{8}{5}M({a}^{2}+10{b}^{2})$

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